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README.md

Convection-diffusion of a Gaussian hill problem

Author: Riccardo Tosi

Kratos version: 8.0

Source files: source

Case Specification

This example is taken from [Donea, J., & Huerta, A. (2003). Finite Element Methods for Flow Problems. Section 5.6.1] and adapted to run on a two-dimensional mesh. We solve the transient convection diffusion equation , where specific initial conditions are set. We refer to the above reference for further details.

The problem is solved exploiting the Runge-Kutta 4 time integration explicit method, and it can be run with four different stabilizations:

  • quasi-static algebraic subgrid scale (QSASGS)
  • quasi-static orthogonal subgrid scale (QSOSS)
  • dynamic algebraic subgrid scale (DASGS)
  • dynamic orthogonal subgrid scale (DOSS)

Results

We present the temporal evolution of for the DOSS case.

temperature

We can observe the results we obtain are consistent with both the reference [Donea, J., & Huerta, A. (2003). Finite Element Methods for Flow Problems. Section 5.6.1].

Moreover, we also compared our numerical solution against the analytical solution , where , , the diffusivity, , the convective velocity and the simulation time. All physical quantities unit measures are expressed according to the Convection Diffusion application and the materials.json file. The norm we obtain is 0.001575 for the DOSS element.